Question $9[10$ marks$]$

We conduct the linear regression to analyze the relationship between speed $($ Y $)$ and density $($ X $),$ and the regression results are presented in the following table. Please

$1)$ Suppose the speed and density follow the Greenshield's model Speed $\backslash (=$v$\_\{$f$\}\backslash$left$(1-\backslash$frac$\{\backslash$text $\{$ Density $\}\}\{$k$\_\{$j$\}\}\backslash$right$)\backslash ).$ Please calculate what is $\backslash ($ v$\_\{$f$\}\backslash )$ and $\backslash ($ k$\_\{$j$\}\backslash )$ based on the regression results. $[3$ marks$].$

$2)$ Calculate the missing value $($a$)$ in the following table, show your steps $[2$ marks$].$

$3)$ Calculate the missing values $($b$)$ and $($c$)$ in the following table, show your steps $[2$ marks$).$

$4)$ Calculate the missing value $($d$)$ in the table below, show your steps $[3$ marks$].$